In triangle ABC, if angle A = 45 degrees, angle B = 45 degrees, and side a = 10

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Question: In triangle ABC, if angle A = 45 degrees, angle B = 45 degrees, and side a = 10 cm, what is the length of side c?

Options:

Correct Answer: 10√2 cm

Solution:

In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Thus, c = a√2 = 10√2 cm.

In triangle ABC, if angle A = 45 degrees, angle B = 45 degrees, and side a = 10 cm, what is the length of side c?

In triangle ABC, if angle A = 45 degrees, angle B = 45 degrees, and side a = 10 cm, what is the length of side c?

Step 1: Identify the type of triangle. Since angle A and angle B are both 45 degrees, triangle ABC is an isosceles right triangle.
Step 2: Recall the properties of an isosceles right triangle. In this type of triangle, the sides opposite the 45-degree angles are equal.
Step 3: Note that side a (which is opposite angle A) is given as 10 cm.
Step 4: In an isosceles right triangle, the length of the hypotenuse (side c) can be found using the formula: c = a√2.
Step 5: Substitute the value of side a into the formula: c = 10√2 cm.
Step 6: Calculate the length of side c, which is approximately 14.14 cm.

Isosceles Right Triangle Properties – In an isosceles right triangle, the angles are 45-45-90 degrees, and the sides opposite these angles are equal, with the hypotenuse being the length of a leg multiplied by √2.